We are given the following statement about the measures of some angles in the diagram.
If the measure of angle ∠ 1=123^(∘), then the measure of ∠ 7= .
When a transversal intersects parallel lines, the alternate exterior angles are congruent. Alternate exterior angles are the angles that lie on the outside of the parallel lines and on opposite sides of a transversal. In this case, lines r and s are parallel lines which are cut by the transversal t. Let's take a look at the given diagram.
We can see that ∠ 1 and ∠ 7 lie on the outside of the lines r and s and on opposite sides of the transversal t. This means they are alternate exterior angles, so they are congruent. Congruent angles are angles which have the same measure, so the measure of ∠ 7 is the same as the measure of ∠ 1.
∠ 1=∠ 7=123^(∘)
With this in mind, we can complete our statement.
If the measure of angle ∠ 1=123^(∘), then the measure of ∠ 7=123^(∘).
